Download presentation

Presentation is loading. Please wait.

Published byDimitri Slaton Modified over 9 years ago

1
Electric Potential AP Physics Montwood High School R. Casao

2
Electric Potential of a Sphere Consider a conducting spherical shell of radius R. If the shell carries a charge +Q, the charge will lie on the outer surface of the shell and the electric field inside the sphere will be 0 N/C (Q in = 0 C).

3
Electric Potential of a Sphere At points outside the shell, the electric field exists as if all of the charge were concentrated at the center (like a point charge) for r > R

4
Electric Potential of a Sphere For points inside the shell: –Since the electric field = 0 N/C inside the shell, there is no electric force and no work done on a charge moving inside the shell. The potential is constant within the sphere. So if we move a charge q from the surface of the sphere to its inside, the potential in J/C would not change. The potential everywhere inside the shell is equal to the potential on the surface. for r < R

5
Electric Potential of a Sphere These two conditions also apply to a solid conducting sphere.

6
Electric Potential of a Nonconducting (Insulating) Sphere If a nonconducting (or insulating) sphere of radius R has a charge of +Q distributed uniformly throughout its volume (charge density is constant). At points outside the sphere: –The electric field exists as if all of the charge were concentrated at the center (like a point charge) for r > R

7
Electric Potential of a Nonconducting (Insulating) Sphere At points inside the sphere, uniform charge density allows us to set up the proportional relationship b/w charge and volume to determine the charge contained within the sphere of radius r:

8
Electric Potential of a Nonconducting (Insulating) Sphere From Gauss’ Law :

9
Electric Potential of a Nonconducting (Insulating) Sphere Using : And moving from the outer surface R of the sphere inside to the location of radius r:

10
Electric Potential of a Nonconducting (Insulating) Sphere

11
Replace the V R equation: Add to both sides:

12
Electric Potential of a Nonconducting (Insulating) Sphere Multiply by 2·R 2 to get a common denominator of 2·R 3.

13
Electric Potential of a Nonconducting (Insulating) Sphere Factor out

14
The Potential of a Cylinder Consider a cylinder of radius R which carries a uniform charge density . The electric field at a distance r from the center of the cylinder is: In a problem like this, the potential is 0 V at a position some distance away from the cylinder. At r = a, V a = 0 V.

15
The Potential of a Cylinder Using Integrate from a to r.

16
The Potential of a Cylinder

17
Use the properties of logarithms (divide):

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google